/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        arm_mat_inverse_f64.c
 * Description:  Floating-point matrix inverse
 *
 * $Date:        18. March 2019
 * $Revision:    V1.6.0
 *
 * Target Processor: Cortex-M cores
 * -------------------------------------------------------------------- */
/*
 * Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
 *
 * SPDX-License-Identifier: Apache-2.0
 *
 * Licensed under the Apache License, Version 2.0 (the License); you may
 * not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an AS IS BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#include "arm_math.h"

/**
  @ingroup groupMatrix
 */


/**
  @addtogroup MatrixInv
  @{
 */

/**
  @brief         Floating-point (64 bit) matrix inverse.
  @param[in]     pSrc      points to input matrix structure. The source matrix is modified by the function.
  @param[out]    pDst      points to output matrix structure
  @return        execution status
                   - \ref ARM_MATH_SUCCESS       : Operation successful
                   - \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed
                   - \ref ARM_MATH_SINGULAR      : Input matrix is found to be singular (non-invertible)
 */

arm_status arm_mat_inverse_f64(
	const arm_matrix_instance_f64 *pSrc,
	arm_matrix_instance_f64 *pDst)
{
	float64_t *pIn = pSrc->pData;                  /* input data matrix pointer */
	float64_t *pOut = pDst->pData;                 /* output data matrix pointer */
	float64_t *pInT1, *pInT2;                      /* Temporary input data matrix pointer */
	float64_t *pOutT1, *pOutT2;                    /* Temporary output data matrix pointer */
	float64_t *pPivotRowIn, *pPRT_in, *pPivotRowDst, *pPRT_pDst;  /* Temporary input and output data matrix pointer */
	uint32_t numRows = pSrc->numRows;              /* Number of rows in the matrix  */
	uint32_t numCols = pSrc->numCols;              /* Number of Cols in the matrix  */

#if defined (ARM_MATH_DSP)

	float64_t Xchg, in = 0.0, in1;                /* Temporary input values  */
	uint32_t i, rowCnt, flag = 0U, j, loopCnt, k, l;      /* loop counters */
	arm_status status;                             /* status of matrix inverse */

#ifdef ARM_MATH_MATRIX_CHECK

	/* Check for matrix mismatch condition */
	if ((pSrc->numRows != pSrc->numCols) ||
		(pDst->numRows != pDst->numCols) ||
		(pSrc->numRows != pDst->numRows)) {
		/* Set status as ARM_MATH_SIZE_MISMATCH */
		status = ARM_MATH_SIZE_MISMATCH;
	} else

#endif /* #ifdef ARM_MATH_MATRIX_CHECK */

	{

		/*--------------------------------------------------------------------------------------------------------------
		 * Matrix Inverse can be solved using elementary row operations.
		 *
		 *  Gauss-Jordan Method:
		 *
		 *      1. First combine the identity matrix and the input matrix separated by a bar to form an
		 *        augmented matrix as follows:
		 *                      _                  _         _         _
		 *                     |  a11  a12 | 1   0  |       |  X11 X12  |
		 *                     |           |        |   =   |           |
		 *                     |_ a21  a22 | 0   1 _|       |_ X21 X21 _|
		 *
		 *      2. In our implementation, pDst Matrix is used as identity matrix.
		 *
		 *      3. Begin with the first row. Let i = 1.
		 *
		 *      4. Check to see if the pivot for row i is zero.
		 *         The pivot is the element of the main diagonal that is on the current row.
		 *         For instance, if working with row i, then the pivot element is aii.
		 *         If the pivot is zero, exchange that row with a row below it that does not
		 *         contain a zero in column i. If this is not possible, then an inverse
		 *         to that matrix does not exist.
		 *
		 *      5. Divide every element of row i by the pivot.
		 *
		 *      6. For every row below and  row i, replace that row with the sum of that row and
		 *         a multiple of row i so that each new element in column i below row i is zero.
		 *
		 *      7. Move to the next row and column and repeat steps 2 through 5 until you have zeros
		 *         for every element below and above the main diagonal.
		 *
		 *      8. Now an identical matrix is formed to the left of the bar(input matrix, pSrc).
		 *         Therefore, the matrix to the right of the bar is our solution(pDst matrix, pDst).
		 *----------------------------------------------------------------------------------------------------------------*/

		/* Working pointer for destination matrix */
		pOutT1 = pOut;

		/* Loop over the number of rows */
		rowCnt = numRows;

		/* Making the destination matrix as identity matrix */
		while (rowCnt > 0U) {
			/* Writing all zeroes in lower triangle of the destination matrix */
			j = numRows - rowCnt;
			while (j > 0U) {
				*pOutT1++ = 0.0;
				j--;
			}

			/* Writing all ones in the diagonal of the destination matrix */
			*pOutT1++ = 1.0;

			/* Writing all zeroes in upper triangle of the destination matrix */
			j = rowCnt - 1U;
			while (j > 0U) {
				*pOutT1++ = 0.0;
				j--;
			}

			/* Decrement loop counter */
			rowCnt--;
		}

		/* Loop over the number of columns of the input matrix.
		   All the elements in each column are processed by the row operations */
		loopCnt = numCols;

		/* Index modifier to navigate through the columns */
		l = 0U;

		while (loopCnt > 0U) {
			/* Check if the pivot element is zero..
			 * If it is zero then interchange the row with non zero row below.
			 * If there is no non zero element to replace in the rows below,
			 * then the matrix is Singular. */

			/* Working pointer for the input matrix that points
			 * to the pivot element of the particular row  */
			pInT1 = pIn + (l * numCols);

			/* Working pointer for the destination matrix that points
			 * to the pivot element of the particular row  */
			pOutT1 = pOut + (l * numCols);

			/* Temporary variable to hold the pivot value */
			in = *pInT1;

			/* Destination pointer modifier */
			k = 1U;

			/* Check if the pivot element is zero */
			if (*pInT1 == 0.0) {
				/* Loop over the number rows present below */
				for (i = (l + 1U); i < numRows; i++) {
					/* Update the input and destination pointers */
					pInT2 = pInT1 + (numCols * i);
					pOutT2 = pOutT1 + (numCols * k);

					/* Check if there is a non zero pivot element to
					 * replace in the rows below */
					if (*pInT2 != 0.0) {
						/* Loop over number of columns
						 * to the right of the pilot element */
						j = numCols - l;

						while (j > 0U) {
							/* Exchange the row elements of the input matrix */
							Xchg = *pInT2;
							*pInT2++ = *pInT1;
							*pInT1++ = Xchg;

							/* Decrement the loop counter */
							j--;
						}

						/* Loop over number of columns of the destination matrix */
						j = numCols;

						while (j > 0U) {
							/* Exchange the row elements of the destination matrix */
							Xchg = *pOutT2;
							*pOutT2++ = *pOutT1;
							*pOutT1++ = Xchg;

							/* Decrement loop counter */
							j--;
						}

						/* Flag to indicate whether exchange is done or not */
						flag = 1U;

						/* Break after exchange is done */
						break;
					}

					/* Update the destination pointer modifier */
					k++;

					/* Decrement loop counter */
					i--;
				}
			}

			/* Update the status if the matrix is singular */
			if ((flag != 1U) && (in == 0.0)) {
				return ARM_MATH_SINGULAR;
			}

			/* Points to the pivot row of input and destination matrices */
			pPivotRowIn = pIn + (l * numCols);
			pPivotRowDst = pOut + (l * numCols);

			/* Temporary pointers to the pivot row pointers */
			pInT1 = pPivotRowIn;
			pInT2 = pPivotRowDst;

			/* Pivot element of the row */
			in = *pPivotRowIn;

			/* Loop over number of columns
			 * to the right of the pilot element */
			j = (numCols - l);

			while (j > 0U) {
				/* Divide each element of the row of the input matrix
				 * by the pivot element */
				in1 = *pInT1;
				*pInT1++ = in1 / in;

				/* Decrement the loop counter */
				j--;
			}

			/* Loop over number of columns of the destination matrix */
			j = numCols;

			while (j > 0U) {
				/* Divide each element of the row of the destination matrix
				 * by the pivot element */
				in1 = *pInT2;
				*pInT2++ = in1 / in;

				/* Decrement the loop counter */
				j--;
			}

			/* Replace the rows with the sum of that row and a multiple of row i
			 * so that each new element in column i above row i is zero.*/

			/* Temporary pointers for input and destination matrices */
			pInT1 = pIn;
			pInT2 = pOut;

			/* index used to check for pivot element */
			i = 0U;

			/* Loop over number of rows */
			/*  to be replaced by the sum of that row and a multiple of row i */
			k = numRows;

			while (k > 0U) {
				/* Check for the pivot element */
				if (i == l) {
					/* If the processing element is the pivot element,
					   only the columns to the right are to be processed */
					pInT1 += numCols - l;

					pInT2 += numCols;
				} else {
					/* Element of the reference row */
					in = *pInT1;

					/* Working pointers for input and destination pivot rows */
					pPRT_in = pPivotRowIn;
					pPRT_pDst = pPivotRowDst;

					/* Loop over the number of columns to the right of the pivot element,
					   to replace the elements in the input matrix */
					j = (numCols - l);

					while (j > 0U) {
						/* Replace the element by the sum of that row
						   and a multiple of the reference row  */
						in1 = *pInT1;
						*pInT1++ = in1 - (in * *pPRT_in++);

						/* Decrement the loop counter */
						j--;
					}

					/* Loop over the number of columns to
					   replace the elements in the destination matrix */
					j = numCols;

					while (j > 0U) {
						/* Replace the element by the sum of that row
						   and a multiple of the reference row  */
						in1 = *pInT2;
						*pInT2++ = in1 - (in * *pPRT_pDst++);

						/* Decrement loop counter */
						j--;
					}

				}

				/* Increment temporary input pointer */
				pInT1 = pInT1 + l;

				/* Decrement loop counter */
				k--;

				/* Increment pivot index */
				i++;
			}

			/* Increment the input pointer */
			pIn++;

			/* Decrement the loop counter */
			loopCnt--;

			/* Increment the index modifier */
			l++;
		}


#else

	float64_t Xchg, in = 0.0;                     /* Temporary input values  */
	uint32_t i, rowCnt, flag = 0U, j, loopCnt, k, l;      /* loop counters */
	arm_status status;                             /* status of matrix inverse */

#ifdef ARM_MATH_MATRIX_CHECK

	/* Check for matrix mismatch condition */
	if ((pSrc->numRows != pSrc->numCols) ||
		(pDst->numRows != pDst->numCols) ||
		(pSrc->numRows != pDst->numRows)) {
		/* Set status as ARM_MATH_SIZE_MISMATCH */
		status = ARM_MATH_SIZE_MISMATCH;
	} else

#endif /* #ifdef ARM_MATH_MATRIX_CHECK */

	{

		/*--------------------------------------------------------------------------------------------------------------
		 * Matrix Inverse can be solved using elementary row operations.
		 *
		 *  Gauss-Jordan Method:
		 *
		 *      1. First combine the identity matrix and the input matrix separated by a bar to form an
		 *        augmented matrix as follows:
		 *                      _  _          _     _      _   _         _         _
		 *                     |  |  a11  a12  | | | 1   0  |   |       |  X11 X12  |
		 *                     |  |            | | |        |   |   =   |           |
		 *                     |_ |_ a21  a22 _| | |_0   1 _|  _|       |_ X21 X21 _|
		 *
		 *      2. In our implementation, pDst Matrix is used as identity matrix.
		 *
		 *      3. Begin with the first row. Let i = 1.
		 *
		 *      4. Check to see if the pivot for row i is zero.
		 *         The pivot is the element of the main diagonal that is on the current row.
		 *         For instance, if working with row i, then the pivot element is aii.
		 *         If the pivot is zero, exchange that row with a row below it that does not
		 *         contain a zero in column i. If this is not possible, then an inverse
		 *         to that matrix does not exist.
		 *
		 *      5. Divide every element of row i by the pivot.
		 *
		 *      6. For every row below and  row i, replace that row with the sum of that row and
		 *         a multiple of row i so that each new element in column i below row i is zero.
		 *
		 *      7. Move to the next row and column and repeat steps 2 through 5 until you have zeros
		 *         for every element below and above the main diagonal.
		 *
		 *      8. Now an identical matrix is formed to the left of the bar(input matrix, src).
		 *         Therefore, the matrix to the right of the bar is our solution(dst matrix, dst).
		 *----------------------------------------------------------------------------------------------------------------*/

		/* Working pointer for destination matrix */
		pOutT1 = pOut;

		/* Loop over the number of rows */
		rowCnt = numRows;

		/* Making the destination matrix as identity matrix */
		while (rowCnt > 0U) {
			/* Writing all zeroes in lower triangle of the destination matrix */
			j = numRows - rowCnt;
			while (j > 0U) {
				*pOutT1++ = 0.0;
				j--;
			}

			/* Writing all ones in the diagonal of the destination matrix */
			*pOutT1++ = 1.0;

			/* Writing all zeroes in upper triangle of the destination matrix */
			j = rowCnt - 1U;
			while (j > 0U) {
				*pOutT1++ = 0.0;
				j--;
			}

			/* Decrement loop counter */
			rowCnt--;
		}

		/* Loop over the number of columns of the input matrix.
		   All the elements in each column are processed by the row operations */
		loopCnt = numCols;

		/* Index modifier to navigate through the columns */
		l = 0U;

		while (loopCnt > 0U) {
			/* Check if the pivot element is zero..
			 * If it is zero then interchange the row with non zero row below.
			 * If there is no non zero element to replace in the rows below,
			 * then the matrix is Singular. */

			/* Working pointer for the input matrix that points
			 * to the pivot element of the particular row  */
			pInT1 = pIn + (l * numCols);

			/* Working pointer for the destination matrix that points
			 * to the pivot element of the particular row  */
			pOutT1 = pOut + (l * numCols);

			/* Temporary variable to hold the pivot value */
			in = *pInT1;

			/* Destination pointer modifier */
			k = 1U;

			/* Check if the pivot element is zero */
			if (*pInT1 == 0.0) {
				/* Loop over the number rows present below */
				for (i = (l + 1U); i < numRows; i++) {
					/* Update the input and destination pointers */
					pInT2 = pInT1 + (numCols * i);
					pOutT2 = pOutT1 + (numCols * k);

					/* Check if there is a non zero pivot element to
					 * replace in the rows below */
					if (*pInT2 != 0.0) {
						/* Loop over number of columns
						 * to the right of the pilot element */
						for (j = 0U; j < (numCols - l); j++) {
							/* Exchange the row elements of the input matrix */
							Xchg = *pInT2;
							*pInT2++ = *pInT1;
							*pInT1++ = Xchg;
						}

						for (j = 0U; j < numCols; j++) {
							Xchg = *pOutT2;
							*pOutT2++ = *pOutT1;
							*pOutT1++ = Xchg;
						}

						/* Flag to indicate whether exchange is done or not */
						flag = 1U;

						/* Break after exchange is done */
						break;
					}

					/* Update the destination pointer modifier */
					k++;
				}
			}

			/* Update the status if the matrix is singular */
			if ((flag != 1U) && (in == 0.0)) {
				return ARM_MATH_SINGULAR;
			}

			/* Points to the pivot row of input and destination matrices */
			pPivotRowIn = pIn + (l * numCols);
			pPivotRowDst = pOut + (l * numCols);

			/* Temporary pointers to the pivot row pointers */
			pInT1 = pPivotRowIn;
			pOutT1 = pPivotRowDst;

			/* Pivot element of the row */
			in = *(pIn + (l * numCols));

			/* Loop over number of columns
			 * to the right of the pilot element */
			for (j = 0U; j < (numCols - l); j++) {
				/* Divide each element of the row of the input matrix
				 * by the pivot element */
				*pInT1 = *pInT1 / in;
				pInT1++;
			}
			for (j = 0U; j < numCols; j++) {
				/* Divide each element of the row of the destination matrix
				 * by the pivot element */
				*pOutT1 = *pOutT1 / in;
				pOutT1++;
			}

			/* Replace the rows with the sum of that row and a multiple of row i
			 * so that each new element in column i above row i is zero.*/

			/* Temporary pointers for input and destination matrices */
			pInT1 = pIn;
			pOutT1 = pOut;

			for (i = 0U; i < numRows; i++) {
				/* Check for the pivot element */
				if (i == l) {
					/* If the processing element is the pivot element,
					   only the columns to the right are to be processed */
					pInT1 += numCols - l;
					pOutT1 += numCols;
				} else {
					/* Element of the reference row */
					in = *pInT1;

					/* Working pointers for input and destination pivot rows */
					pPRT_in = pPivotRowIn;
					pPRT_pDst = pPivotRowDst;

					/* Loop over the number of columns to the right of the pivot element,
					   to replace the elements in the input matrix */
					for (j = 0U; j < (numCols - l); j++) {
						/* Replace the element by the sum of that row
						   and a multiple of the reference row  */
						*pInT1 = *pInT1 - (in * *pPRT_in++);
						pInT1++;
					}

					/* Loop over the number of columns to
					   replace the elements in the destination matrix */
					for (j = 0U; j < numCols; j++) {
						/* Replace the element by the sum of that row
						   and a multiple of the reference row  */
						*pOutT1 = *pOutT1 - (in * *pPRT_pDst++);
						pOutT1++;
					}

				}

				/* Increment temporary input pointer */
				pInT1 = pInT1 + l;
			}

			/* Increment the input pointer */
			pIn++;

			/* Decrement the loop counter */
			loopCnt--;

			/* Increment the index modifier */
			l++;
		}

#endif /* #if defined (ARM_MATH_DSP) */

		/* Set status as ARM_MATH_SUCCESS */
		status = ARM_MATH_SUCCESS;

		if ((flag != 1U) && (in == 0.0)) {
			pIn = pSrc->pData;
			for (i = 0; i < numRows * numCols; i++) {
				if (pIn[i] != 0.0) {
					break;
				}
			}

			if (i == numRows * numCols) {
				status = ARM_MATH_SINGULAR;
			}
		}
	}

	/* Return to application */
	return (status);
}

/**
  @} end of MatrixInv group
 */
